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Slide show
Mathematics
Exercise 13
Surface Area and Volume
Topic on
On

Slide 2

Surface Area and Volume
Vocabulary & Formulas

Slide 3

Prism
Definition:
A three-dimensional solid that has two congruent and parallel faces that are polygons. The remaining faces are rectangles. Prisms are named by their faces.

Slide 4

Rectangular Prism
Definition:
A three-dimensional solid that has two congruent and parallel faces that are rectangles. The remaining faces are rectangles.

Slide 5

Cube
Definition:
A rectangular prism in which all faces are congruent squares.

Slide 6

Surface Area
Definition:
The sum of the areas of all of the faces of a three-dimensional figure.
Ex. How much construction paper will I need to fit on the outside of the shape?

Slide 7

Volume
Definition:
The measure in cubic units of the interior of a solid figure; or the space enclosed by a solid figure.
Ex. How much sand will it hold?

Slide 8

Surface Area of a Rectangular Prism
Ex:
How much construction paper would I need to fit on the outside of a particular rectangular prism?
Formula:
S.A. = 2LW + 2Lh + 2Wh

Slide 9

Surface Area of a Cube
Ex:
How much construction paper would I need to fit on the outside of a particular cube?
Formula:
S.A. = 6s2

Slide 10

Volume of a Rectangular Prism
Ex:
How much sand would I need to fill the inside of a particular rectangular prism?
Formula:
V = L*W*h

Slide 11

Volume of a Cube
Ex:
How much sand would I need to fill the inside of a particular cube?
Formula:
V = s3

Slide 12

Surface area and volume of different Geometrical Figures
Cube
Parallelopiped
Cylinder
Cone

Slide 13

Total faces = 6 ( Here three faces are visible)
Faces of cube

Slide 14

Faces of Parallelopiped
Total faces = 6 ( Here only three faces are visible.)

Slide 15

Total cores = 12 ( Here only 9 cores are visible)
Cores
Note Same is in the case in parallelopiped.

Slide 16

Surface area = Area of all six faces
= 6a2
a
b
Surface area
Cube
Parallelopiped
Surface area = Area of all six faces
= 2(axb + bxc +cxa)
c
a
a
a
Click to see the faces of parallelopiped.
(Here all the faces are square)
(Here all the faces are rectangular)

Volume of Cube
Area of base (square) = a2
Height of cube = a
Volume of cube = Area of base x height
= a2 x a = a3
Click to see
(unit)3

Slide 19

Circumference of circle = 2 π r
Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h)
Outer Curved Surface area of cylinder
Activity -: Keep bangles of same radius one over another. It will form a cylinder.
It is the area covered by the outer surface of a cylinder.
Formation of Cylinder by bangles
Circumference of circle = 2 π r
Click to animate

Total surface Area and volume of different geometrical figures and nature
So for a given total surface area the volume of sphere is maximum. Generally most of the fruits in the nature are spherical in nature because it enables them to occupy less space but contains big amount of eating material.
22r

Slide 31

Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree
Click the next

Slide 32

r
V= 1/3π r2(3r)
V= π r3
Long but Light in weight
Small niddle will require to stick it in the tree,so little harm in tree
V= π r2 (3r)
V= 3 π r3
Long but Heavy in weight
Long niddle will require to stick it in the tree,so much harm in tree
r

Slide 34

V=1/3 πr2h
If h = r then
V=1/3 πr3
r
r
If we make a cone having radius and height equal to the radius of sphere. Then a water filled cone can fill the sphere in 4 times.
V1 = 4V = 4(1/3 πr3)
= 4/3 πr3

Slide 35

4( 1/3πr2h ) = 4( 1/3πr3 ) = V
h=r
Volume of a Sphere
Click to See the experiment
Here the vertical height and radius of cone are same as radius of sphere.
4( volume of cone) = volume of Sphere
V = 4/3 π r3

Summary: this slid show is made by abhinav kumar sinha
class-9th-E
schoo-k.v.no.2 ambala cantt
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